...Because they've got egg on their face, having just lost a political ally to the EU, and they're trying to minimize the damage.
By invading a sovereign nation?
Consider the Russian position: the Ukraine has seen its government overthrown by an opposition movement deeply opposed to Russian influence. The legitimacy of their taking power has not been established, and rather than stabilise the country and set elections, they immediately started distancing themselves from Russia.
On top of that, the Ukraine is a key partner in the export of natural gas from Russia to Western Europe. Two of their major pipelines pass through the Ukraine, who are partners in the ownership and operation of them. On top of that, parts of southern Russia rely on the Ukrainian manufacturing sector; a lot of goods produced in eastern Ukraine are exported to Russia. A move away from Russia by the Ukrainians will hurt all of this, for both sides.
The Crimean Peninsula sits between the Black Sea and the Sea of Azov. At the eastern end of the Sea of Azov is Rostov-on-Don, one of just four major ports within Russia. Of the other three, Murmansk is in the Arctic Circle, and is not good for trading. Vladivostok is just north of the Korean Peninsula, eleven time zones away. It mostly services eastern Russia. The other one is St. Petersberg, which is good. So with a major population concentration in the west of the country, the Russians need Rostov-on-Don (which also sits on the Don River, one of their major waterways), but if the Ukrainians distance themselves from Russia, trading through Rostov-on-Don will become difficult. They will also lose access to the Ukrainian port of Odessa.
Crimea is also home to the Black Sea Fleet, one of the major fleets of the Russian Navy. Losing access to Crimea would mean the Russian military presence in the area would be significantly reduced.
Finally, one of the key issues in the protest movement was the choice between aligning with the EU, or closer ties with Russia. Those in favour of joining the EU felt that a relationship with Russia would hurt them economically. Likewise, those in favour of getting closer to Russia felt that moving to the EU would hurt them. The new government in Kiev made their intentions fairly well known, and a lot of ethnic Russians felt that their fears were being realised and that the new government was marginalising them.
Given that there us so much economic, socio-political and military future at stake, Russia is pretty much forced to have a position on what is happening in the Ukraine. How they choose to act on that position is open to debate, but the events in the Ukraine have had significant consequences for Russia. After all, less than two weeks ago, the world was singing their praises for Russia after the Olympics. Putin has already burnt up all of that goodwill in less than twenty-four hours, which is not something than you would do on a whim. Why risk international condemnation like that unless there was something serious at stake? In the worst-case scenario for Russia, the government in Kiev could completely cut ties with Moscow, and Russia loses its ability to import goods through the Black Sea and export gas to Europe. Given that they just spent $51 billion on the Olympics, Russia could be staring down the barrel of a major recession. After all, one of the reasons why Greece went into an economic crisis was because they could not afford to pay their debts over the 2004 Olympics.
